Question

A floor is 5m long and 4m wide. A square carpet of sides 3 m is laid on the floor . Find the area of the floor that is not carpeted.

Answer 1

$\huge\mathbb{SOLUTION:-}$

$\sf\underline{\pink{\:\:\:\:\:\:\:Given:-\:\:\:\:\:\:\:}}$

$\sf\bullet Dimensions\:of\:floor=4m\:and\:5m\\ \\ \sf\bullet Dimensions\:of\:Carpet=3m$

Formula used

$\boxed{\sf{Area\:of\: rectangle=length\times breadth}}$

$\boxed{\sf{Area\:of\:square=side{}^{2}}}$

Now

$\sf\underline{\blue{\:\:\:\:\:\:\:A.T.Q:-\:\:\:\:\:\:\:}}$

First the Area of floor

$\sf:\implies Area\:of\:Floor=4\times 5\\ \\ \sf:\implies Area\:of\:Floor=20m{}^{2}$

Now The area of Carpet

$\sf:\implies Area\:of\: carpet=(3m){}^{2}\\ \\ \sf:\implies Area\:of\:carpet= 9m{}^{2}$

• Now we have to find the Area of floor which is not carpeted

$\sf \bullet{\purple{\underline{Area\:of\:floor\: not\:carpeted= Area\:of\:floor-Area\:of\:carpet}}}$

$\sf:\implies Area\:of\:floor\:Not\:carpeted= 20m{}^{2}-9m{}^{2}\\ \\ \sf:\implies Not\:carpeted=11m{}^{2}$

$\boxed{\sf{\red{Area\:of\:not\:carpeted\:floor=11m{}^{2}}}}$

Answer 2

Answer:

$\large\boxed{\sf{11\;{m}^{2}}}$

Step-by-step explanation:

Given dimension of floor;

• Length, l = 5 m
• Breadth, b = 4 m

We know that, area of rectangle = lb

.°. Area of floor = 5 × 4 = $20\;{m}^{2}$

Now, Length of each side of carpet, a= 3 m

We know that, area of square = (a × a)

.°. Area of carpet = 3 × 3 = $9\;{m}^{2}$

.°. Area of floor not carpeted = 20 - 9

Hence , required area = $11\:{m}^{2}$